On the connections of the generalized entropies and Kolmogorov-Sinai entropies

TL;DR

This paper explores the relationship between generalized measure-theoretic entropies, defined via arbitrary concave functions, and Kolmogorov-Sinai entropy, showing a linear dependence under certain conditions.

Contribution

It establishes that generalized entropies, using a broad class of concave functions, are linearly related to Kolmogorov-Sinai entropy, extending the understanding of entropy invariants.

Findings

Generalized measure-theoretic entropies depend linearly on Kolmogorov-Sinai entropy.

The results hold under mild assumptions on the concave function used.

The work broadens the conceptual framework linking different entropy measures.

Abstract

We consider the concept of generalized measure-theoretic entropy, where instead of the Shannon entropy function we consider an arbitrary concave function defined on the unit interval, vanishing in the origin. Under mild assumptions on this function we show that this isomorphism invariant is linearly dependent on the Kolmogorov-Sinai entropy.